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  • Provide solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 18

Provide solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 18

Answers (1)

Answer:

        0

Hint:

You must know about derivative of

        cos\: \theta\: and\: tan\: \theta

Given:

        I\! f\: y=sin(sin\: x)

        \begin{aligned} &Prove\: \: that\: \: \frac{d^{2} y}{d x^{2}}+\tan x \frac{d y}{d x}+y \cos ^{2} x =0\\ \end{aligned}

Solution:

Let\: y=sin(sin\: x)

        \begin{aligned} &\frac{d y}{d x}=\cos (\sin x) \cdot \cos x \\ &\frac{d^{2} y}{d x^{2}}=-\cos (\sin x)(\sin x)+\cos x(-\sin (\sin x) \cos x) \\ &\frac{d^{2} y}{d x^{2}}=-\sin x \cos (\sin x)-\cos ^{2} x(\sin (\sin x)) \end{aligned}

        \begin{aligned} &L H S:-\frac{d^{2} y}{d x^{2}}+\tan x \frac{d y}{d x}+y \cos ^{2} x \\ &-\sin x \cos (\sin x)-\cos ^{2} x(\sin (\sin x))+\tan x \cos x \cos (\sin x)+\sin (\sin x) \cos ^{2} x \\ &-\sin x(\cos (\sin x))+\frac{\sin x}{\cos x} \cdot \cos x \cdot \cos (\sin x) \\ &-\sin x \cos x \sin x+\sin x \cos x \sin x \end{aligned}

Hence proved

Posted by

Gurleen Kaur

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